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DOI: 10.1007/s00208-002-0400-y Math. Ann. (2003) MathematischeAnnalen
 

Summary: DOI: 10.1007/s00208-002-0400-y
Math. Ann. (2003) MathematischeAnnalen
Young's inequality in trace-class operators
Mart´in Argerami · Douglas R. Farenick
Received: 20 December 2001 / Revised version: 11 July 2002 /
Published online: 10 February 2003 ­ © Springer-Verlag 2003
Abstract. If a and b are trace-class operators, and if u is a partial isometry, then u | ab|u
1
1
p |a|p
+ 1
q |b|q
1, where · 1 denotes the norm in the trace class. The present paper characte-
rises the cases of equality in this Young inequality, and the characterisation is examined in the
context of both the operator and the Hilbert­Schmidt forms of Young's inequality.
Mathematics Subject Classification (2000): 47A63, 15A60
1. Introduction
Building on the work by T. Ando [A], it was shown in [EFZ] that for each pair of
compact operators a and b, and for each p, q R+
for which 1/p + 1/q = 1,

  

Source: Argerami, Martin - Department of Mathematics and Statistics, University of Regina

 

Collections: Mathematics